LABORATORY MATERIAL EE0211 – ELECTRICAL CIRCUITS LAB

DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING FACULTY OF ENGINEERING & TECHNOLOGY SRM UNIVERSITY, Kattankulathur – 603 203

1

CONTENTS Sl.No.

Name of the Experiments

Page No.

1

Verification of Kirchoff’s laws

3

2

Verification of Superposition theorem

6

3

Verification of Thevenin’s & Norton’s Theorem

9

4

Verification of Maximum Power Transfer theorem

15

5

Power measurement in 3 phase unbalanced circuits

19

6

Power measurement in 3 phase balanced circuits

20

7

Power measurement using 3 voltmeter & 3 ammeter

22

method 8

Circuit analysis using CRO

26

9

Circuit transients by digital simulation

28

10

Study of resonance

30

2

Experiment No. 1 Date :

VERIFICATION OF KIRCHHOFFS LAWS

Aim: To verify Kirchhoff’s current law and Kirchhoff’s voltage law for the given circuit. Apparatus Required: Sl.No. Apparatus 1 RPS (regulated power supply) 2 Resistance 3 Ammeter 4 Voltmeter 5 Bread Board & Wires

Range (0-30V) 330, 220 1k (0-30mA)MC (0-30V)MC --

Statement: KCL: The algebraic sum of the currents meeting at a node is equal to zero. KVL: In any closed path / mesh, the algebraic sum of all the voltages is zero. Precautions: 1. Voltage control knob should be kept at minimum position. 2. Current control knob of RPS should be kept at maximum position. Procedure for KCL: 1. Give the connections as per the circuit diagram. 2. Set a particular value in RPS. 3. Note down the corresponding ammeter reading 4. Repeat the same for different voltages Procedure for KVL: 1. Give the connections as per the circuit diagram. 2. Set a particular value in RPS. 3. Note all the voltage reading 4. Repeat the same for different voltages Circuit - KCL

3

Quantity 2 6 3 3 Required

Circuit - KVL

KCL - Theoretical Values: Sl. Voltage No. E Volts 1 5 2 10 3 15 4 20 5 25

KCL - Practical Values: Sl. Voltage No. E Volts 1 5 2 15 3 25

KVL – Theoretical Values Sl.No. RPS E1 E2 V V 1 5 5 2 10 10 3 15 15 4 20 20 5 25 25

I1 mA 5.68 11.3 17.05 22.73 28.42

Current I2 mA 3.12 6.18 9.37 12.49 15.62

I1 mA 5.6 17.2 28

Current I2 mA 3.1 9.4 15.6

Voltage V2 V 4.41 8.83 13.2 17.67 22.08

V1 V 0.58 1.16 1.75 2.33 2.913

4

I1 = I2 + I3 I3 mA 2.56 5.12 7.68 10.24 12.68

mA 5.68 11.3 17.05 22.075 28.42

I1 = I2 + I3 I3 mA 2.2 7.6 12.7

V3 V 0.583 1.17 1.75 2.33 2.915

mA 5.3 17 28.3

KVL E1 = V1 + V2 V 4.99 9.99 14.95 20 24.993

KVL - Practical Values Sl.No. RPS E1 E2 V V 1 5 5 2 10 10 3 15 15

Voltage V2 V 4.4 8.83 13.20

V1 V 0.6 1.13 1.72

V3 V 0.56 1.19 1.78

KVL E1 = V1 + V2 V 5 9.96 14.92

Model Calculations:

Result: Thus Kirchoff’s voltage load and Kirchoff’s current law verified both theoretically and practically.

5

Experiment No. 2 Date :

VERIFICATION OF SUPERPOSITION THEOREM

Aim: To verify the superposition theorem for the given circuit. Apparatus Required: Sl.No. Apparatus 1 RPS (regulated power supply) 2 Ammeter 3 Resistors 4 Bread Board 5 Wires

Range (0-30V) (0-10mA) 1k, 330, 220 ---

Quantity 2 1 3 -Required

Statement: Superposition theorem states that in a linear bilateral network containing more than one source, the current flowing through the branch is the algebraic sum of the current flowing through that branch when sources are considered one at a time and replacing other sources by their respective internal resistances.

Precautions: 1. 2.

Voltage control knob should be kept at manimum position current control knob of RPS should be kept at maximum position

Procedure: 1. Give the connections as per the diagram. 2. Set a particular voltage value using RPS1 and RPS2 & note down the ammeter reading 3. Set the same voltage in circuit I using RPS1 alone and short circuit the terminals and note the ammeter reading. 4. Set the same voltage in RPS2 alone as in circuit I and note down the ammeter reading. 5. Verify superposition theorem.

6

CIRCUIT - 1

CIRCUIT - 2

CIRCUIT - 3 TABULAR COLUMN Theoretical Values Circuit – 1

1 10 V

RPS 2 10 V

Ammeter Reading (I) mA I = 8.83

Circuit – 2

10 V

0V

I’= 3.5

Circuit – 3

0V

10 V

I”= 5.3 I = I’  I” = 8.83

Practical Values RPS Circuit – 1

1 10 V

2 10 V

Ammeter Reading (I) mA I = 8.5

Circuit – 2

10 V

0V

I’= 3.5

Circuit – 3

0V

10 V

I”= 5 I = I’  I” = 8.5 mA = 3.5 + 5 = 8.5 mA

7

Model Calculations:

Result: Superposition theorem have been verified theoretically and practically.

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VERIFICATION OF THEVENIN’S THEOREM

Experiment No. 3 Date : Aim:

To verify Thevenin’s theorem and to find the full load current for the given circuit. Apparatus Required: Sl.No. 1 2 3 4 5

Apparatus RPS (regulated power supply) Ammeter Resistors Bread Board DRB

Range (0-30V) (0-10mA) 1K, 330 ---

Quantity 2 1 3,1 Required 1

Statement: Any linear bilateral, active two terminal network can be replaced by a equivalent voltage source (VTH). Thevenin’s voltage or VOC in series with looking pack resistance RTH. Precautions: 1. Voltage control knob of RPS should be kept at minimum position. 2. Current control knob of RPS should be kept at maximum position Procedure: 1. Connections are given as per the circuit diagram. 2. Set a particular value of voltage using RPS and note down the corresponding ammeter readings. To find VTH 3. Remove the load resistance and measure the open circuit voltage using multimeter (VTH). To find RTH 4. To find the Thevenin’s resistance, remove the RPS and short circuit it and find the RTH using multimeter. 5. Give the connections for equivalent circuit and set VTH and RTH and note the corresponding ammeter reading. 6. Verify Thevenins theorem. Theoretical and Practical Values E(V)

VTH(V)

RTH()

Theoretical

10

5

495

Practical

10

4.99

484

9

IL (mA) Circuit - I Equivalent Circuit 3.34 3.34 3.3

3.36

Circuit - 1 : To find load current

To find VTH

To find RTH

Thevenin’s Equivalent circuit:

10

Model Calculations:

Result: Hence the Thevenin’s theorem is verified both practically and theoretically

11

VERIFICATION OF NORTON’S THEOREM

Experiment No. 4 Date :

Aim: To verify Norton’s theorem for the given circuit. Apparatus Required: Sl.No. 1 Ammeter 2 3 4 5

Apparatus

Range (0-10mA) MC (0-30mA) MC 330, 1K (0-30V) ---

Resistors RPS Bread Board Wires

Quantity 1 1 3,1 2 1 Required

Statement: Any linear, bilateral, active two terminal network can be replaced by an equivalent current source (IN) in parallel with Norton’s resistance (RN)

Precautions: 1. Voltage control knob of RPS should be kept at minimum position. 2. Current control knob of RPS should be kept at maximum position. Procedure: 1. Connections are given as per circuit diagram. 2. Set a particular value in RPS and note down the ammeter readings in the original circuit. To Find IN: 3. Remove the load resistance and short circuit the terminals. 4. For the same RPS voltage note down the ammeter readings. To Find RN: 5. Remove RPS and short circuit the terminal and remove the load and note down the resistance across the two terminals. Equivalent Circuit: 6. Set IN and RN and note down the ammeter readings. 7. Verify Norton’s theorem.

12

To find load current in circuit 1:

To find IN

To find RN

Norton’s equivalent circuit

Constant current source

13

Theoretical and Practical Values E IN (volts) (mA)

RN ()

IL (mA) Circuit - I

Theoretical Values Practical Values

10

10.10

495

334

Equivalent Circuit 3.34

10

10.4

485

3.4

4

Model Calculations:

Result: Norton’s was verified practically and theoretically

14

Experiment No. 5 Date :

VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM

Aim: To verify maximum power transfer theorem for the given circuit Apparatus Required: Sl.No. 1 2 3 4 5

Apparatus

Range (0-30V) (0-10V) MC 1K, 1.3K, 3 ---

RPS Voltmeter Resistor DRB Bread Board & wires

Quantity 1 1 3 1 Required

Statement: In a linear, bilateral circuit the maximum power will be transferred to the load when load resistance is equal to source resistance. Precautions: 1. Voltage control knob of RPS should be kept at minimum position. 2. Current control knob of RPS should be kept at maximum position. Procedure: Circuit – I 1. Connections are given as per the diagram and set a particular voltage in RPS. 2. Vary RL and note down the corresponding ammeter and voltmeter reading. 3. Repeat the procedure for different values of RL & Tabulate it. 4. Calculate the power for each value of RL. To find VTH: 5. Remove the load, and determine the open circuit voltage using multimeter (VTH) To find RTH: 6. Remove the load and short circuit the voltage source (RPS). 7. Find the looking back resistance (RTH) using multimeter. Equivalent Circuit: 8. Set VTH using RPS and RTH using DRB and note down the ammeter reading. 9. Calculate the power delivered to the load (RL = RTH) 10. Verify maximum transfer theorem.

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Circuit - 1

To find VTH

To find RTH

Thevenin’s Equation Circuit

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Power VS RL

Circuit – I Sl.No. 1

RL () 200

I (mA) 1.3

V(V) 0.27

P=VI (watts) 0.26

2

400

1.2

0.481

0.53

3

600

1.1

0.638

0.707

4

800

1

0.771

0.771

5

1200

0.80

1.083

0.866

6

1300

0.77

1.024

0.788

7

1400

0.74

0.998

0.738

8

1500

0.71

0.968

0.687

RTH () 1320

IL (mA) 0.758

P (milli watts) 0.759

1306

0.77

0.77

To find Thevenin’s equivalent circuit VTH (V) 2002 Theoretical Value 2 Practical Value

17

Model Calculations:

Result: Thus maximum power theorem was verified both practically and theoretically

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Experiment No. 6 Date :

THREE PHASE POWER MEASUREMENT (TWO WATTMETER METHOD)

Aim: To measure the 3-phase active and reactive power by 2 – wattmeter method for (i) resistance load (ii) inductive load Apparatus Required: Sl.No. 1 2 3 4

Apparatus

Range (0-600V) MI (0-20A) MI 600V, 10A, UPF 600V, 10A, LPF

Voltmeter Ammeter Wattmeter Wattmeter

Precautions:  THE TPST switch must be kept open initially.  Load must not be applied while starting. Procedure: (i) – Resistive load 1. 2. 3.

Give the connections as per the circuit diagram. Give the supply by closing TPST switch. Vary the resistance load and note down the corresponding readings.

(ii) Inductive load 1. Give the connections as per the circuit diagram. 2. Give the supply by closing the TPST switch 3. Vary the inductive load and note down the corresponding readings.

for inductive load

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Quantity 1 1 2 2

for resistive load Formulae Used: 1.

Real power = w1 + w2

2.

Reactive power =

3.

Tan  =

4.

Power factor = cos 

3 (w1  w2 )

3 ( w1  w2 ) w1  w2

Two Wattmeter Method : Resistive Load

V (volt)

460 460 460 460 460 460 460 460 460

I (A)

0 1.8 3.7 4.6 5.5 6.3 7.2 8.1 9

MF = Wattmeter Reading (W1) OBS ACT = (watt) OBS X MF (watt) 0 0 70 560 160 1280 200 1600 240 1920 280 2240 320 2560 350 2800 390 3120

MF = Wattmeter Reading (W2) OBS ACT=OBS (watt) x MF (watt) 0 90 180 210 250 290 330 370 410

20

0 720 1440 1680 2000 2320 2640 2960 3280

Power Cos  Real Power (watt)

Reactive power (watt)

0 1280 2720 3280 3920 4560 5200 5760 6400

0 -277.12 -277.12 -138.56 -138.56 -138.56 -138.56 -277.12 -277.12

0 0.977 0.9949 0.999 0.9 0.993 0.996 0.9988 0.990

Two Wattmeter Method : Inductive Load

V (volt)

I (A)

410 410 410 410 410 410

1 2 3 4 5 6

MF = Wattmeter Reading (W1) OBS ACT = (watt) OBS x MF (watt) 11 89 15 120 28 140 43 344 78 624 95 760

MF = Wattmeter Reading (W2) OBS ACT=OBS (watt) x MF (watt) 26 32 53 80 106 132

208 256 424 640 848 1056

Power Cos  Real Power (watt)

Reactive power (watt)

296 376 564 984 1472 1816

-554.26 -443.41 -734.39 -1108.51 -1461.78 -1829.05

0.351 0.647 0.609 0.664 0.708 0.705

Model Calculations:

Result: Thus power for three phase power supply was measured using 2 wattmeter method.

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Experiment No. 7 Date :

POWER MEASUREMENT BY 3 - VOLTMETER

Aim: To measure the power in an inductive circuit, Eg: transformer, by 3- voltmeter method. Apparatus Required: Sl.No. 1 Ammeter 2 Voltmeter 3 4 5 6

Apparatus

Range (0-5A) MI (0-150V) MI (0-300V) MI 230V/115V, 1KVA 100

Transformer Auto Transformer Auto Transformer Rheostat

Quantity 1 2 1 1 1 1

Precaution: 1. The DPST switch must be kept open initially. 2. The auto transformer must be kept at minimum potential position 3. The rheostat must be kept at maximum resistance position. Procedure: 1. Give the connections as per the circuit diagram. 2. Adjust the auto transformer, to bring the rated voltage of the transformer 3. Note down the transformer and voltmeter readings. 4. Vary the rheostat for different values and note down the corresponding meter readings. 3 – Voltmeter Method Sl. I No. (amp) 1 0.2 2 0.6 3 0.8 4 1 5 1.1 6 1.2

Vs (volts) 150 150 150 150 150 150

VR (volts) 15 54 73 86 90 95

VL (volts) 136 120 120 110 105 100

22

P (watts) 25.193 21.99 15.18 17.46 20.625 21.99

Cos  0.82 0.293 0.158 0.158 0.178 0.182

Formulae Used: 1.

Power (P) =

VS2  VR2  VL2 watts 2R

R = VR / I 2.

VS2  VR2  VL2 Cos  = 2 Ve VL

Model Calculations:

Result: The power was measured for given circuit using 3 voltmeter method

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Experiment No. 8 Date :

POWER MEASUREMENT BY 3 - AMMETER

Aim: To measure the power in an inductive circuit, Eg: transformer, by 3- ammeter method. Apparatus Required: Sl.No. 1 Ammeter

Apparatus

2 3 4

Voltmeter Auto transformer Transformer

5

Rheostat

Range (0-2A) MI (0-5A) MI (0-150V) MI 230V/115V 1KVA, 1 100 / 4A

Quantity 2 1 1 1 1 1

Precaution 1. The DPST switch must be kept open initially 2. The autotransformer should be kept at minimum potential position 3. The rheostat should be kept at maximum resistance position

Procedure: 1. Give the connections as per the circuit diagram 2. Adjust the auto transformer, to bring the rated voltage of the transformer 3. Note down the ammeter and voltmeter readings. 4. Vary the rheostat for different values and note 3 – Voltmeter Method Sl. No. 1 2 6 4 5 6

V (volts) 115 115 115 115 115 115

Is (amp) 0.75 0.85 0.95 1.05 1.15 1.25

IR (amp) 0.54 0.6 0.7 0.8 0.9 1

IL (amp) 0.48 0.48 0.48 0.48 0.48 0.46

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R (ohm) 213 191.67 164.3 143.7 127.7 0.46

P (watts) 4.31 912.6 14.9 16.6 18 20.1

Cos  0.07 0.22 0.57 0.3 0.32 0.37

Formulae Used: Power (P) = R

2

I

2 S

 I R2  I L2



R = V / IR Power factor cos  =

I S2  I R2  I L2 2 IR IL

Model Calculations:

Result: Thus power was measured using 3 ammeter method

25

Experiment No. 9 Date :

CIRCUIT ANALYSIS USING CRO

Aim: To measure voltage and current and also to study the phase relationship between supply voltage and current in series RC circuit.

Apparatus Required: Sl.No. 1 2 3 4 5

Apparatus Function generator DMM Resistor Capacitor CRO

Range 200  1 F

Quantity 1 1 1 1 1

Procedure: 1. Connections are given as per the circuit diagram. 2. In the function generator, select “SINE WAVE” as the output and set the frequency to 200 Hz. 3. Adjust the amplitude knob of the function generator until the waveform on the oscilloscope shows 2 Vp. 4. Record the peak voltage across the resistor using CRO. 5. Calculate  from t. 6. Draw the waveform for VS, VR.

Circuit Diagram:

26

Sl.No. 1

Sl.No. 1

Frequency (Hz) 200

VR V 0.4

T (ms) 5

t (ms) 0.3

 deg 21.6 (leading

Frequency (Hz) 0.32

VR V 1.6mA

T (ms) 1.2

t (ms) 750

 deg 7.95

Result: The phase relationship between supply voltage and current in series RC circuit is studied and also the voltage and current are increased practically.

27

Experiment No. 10 Date :

CIRCUIT TRANSIENTS BY SIMULATION IN RL CIRCUIT

Aim: To simulate the RL circuit using Pspice software and to study the transient response

Circuit Diagram:

Simulation Parameter: Vdc = 10 volts, R1 = 50 ohms, L = 100mH

28

Simulation Output: 1.

Transient L wave form

2.

Transient R wave form

Result: Simulation of the RL transient circuit was done

29

Experiment No. 11 Date :

STUDY OF RESOURCE

Aim: To study series and parallel resource in AC circuit Series Resource: An RLC circuit is said to be at re source when voltage and current are in phase with each other and power factor is unity.

Z  R  j( X L  X C ) z At series resource

XL = XC Z=R XL = XC 1 L 

C

2 

1 LC

(2 n fr ) 2 

fr  Power factor cos   Q - factor =

1 LC

1 2 LC

R Z

VC VL  V V

Parallel Resonance: Parallel AC circuit is said to be at resource when voltage and current are in phase with each other and power factor is unity. (i)

ideal parallel circuit f 0 

(ii)

Practical circuit - I f 0 

(iii)

Practical circuit – II f 0 

1 2 u LC

1 2u

1 R2  LC L2 1

2u

 (R ) 2  L / C L  2  ( R IC  L)  L/C

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   